${\mathbb R}$$N$上一类Kirchhoff型方程径向对称正解的存在性

Abstract

Abstract:

In this paper, we discuss a class of Kirchhoff type equation whose energy function may not be of $C^1$ class. This equation is closely related to plasma physics and theories for propagation of laser beams. Using a change of variables, we get a new equivalent equation whose energy function is of $C^1$ class. Using a suitable Banach space and variational method, we prove that there is a positive radial solution to the given equation under proper conditions.

Key words: Kirchhoff type equation, Positive radial solution, Variational method, Banach space

CLC Number:

O175.2

Yihua Deng. Existence of Positive Radial Solution to a Class of Kirchhoff type Equation in ${\mathbb R}$ ^$N$[J].Acta mathematica scientia,Series A, 2021, 41(1): 142-148.

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References 13

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Existence of Positive Radial Solution to a Class of Kirchhoff type Equation in ${\mathbb R}$ ^$N$

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Existence of Positive Radial Solution to a Class of Kirchhoff type Equation in ${\mathbb R}$ ^$N$